Question

A student works at an on- campus job Monday through Friday. The student also participates in intramural volleyball on Tuesdays and Thursdays. Given Events A and B, are the two events mutually exclusive? Explain your answer.

Event A: On a random day of the week, the student is working at their on-campus job.

Event B: On a random day of the week, the student is playing intramural volleyball.​

Answer 1

No, the events are not mutually exclusive because they share the common outcomes of the student working and playing volleyball on certain days.

Explanation:

A and B are mutually exclusive events if they cannot occur at the same time. This means that A and B do not share any outcomes and P(A AND B)=0.

In this case, A and B have outcomes in common since the student both works and plays volleyball on Tuesdays and Thursdays. Thus, the events are not mutually exclusive.